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Firstly we need to assume that we will to roll the earth directly towards the sun. Secondly we will need to roll it twice the distance between the center of the earth and the edge of the sun as the center of mass will be kept in the same position.

The approximate distance between the earth and the sun is 150 million kilometers (disregarding the radius of the sun) hence we would need to roll earth into a sausage like shape that of 300 million kilometers long.

Interestingly, we could calculate the approximate thickness of this 300 million kilometer sausage shaped earth and assuming that we didn't condense the earth: the volume of the earth is around 1.08 trillion kilometers cubed. The volume of a cylinder is \(Vol=\pi r^{2} l\) where Vol is 1.08 trillion kilometers cubed and l is 300 million kilometers long. We can arrive at the average diameter of this 300 million kilometer long sausage as: \(D=\sqrt{\frac{1.08 \times 10^{12}}{300 \times 10^{6} \times \pi}}\) which is approximately 66 kilometers wide.